Hi, yesterday we talked about the courage it
takes to step into a difficult conversation by
suggesting different starting points. But what
happens when we do not speak up? What happens
if we do not follow through on our intuitions?
What if we ignore our curious doubts? What if
we just let certainty rule the day? From my experience,
when I ignore my questions and let certainty
be the only voice, I can feel my mind close.
Oxygen gets sucked up. Of course, certainty is
not always bad. In math, certainty feels powerful.
Once something is proven, it is settled. And
that clarity is beautiful. But we've learned
that math also reminds us there is more to the
story on certainty. Every result depends on where
we start. And when that starting point changes,
a different, yet still logical, result can appear.
The surprise is not error. The surprise is expansion.
We saw that in geometry when we changed the parallel
postulate. This is not just an isolated example.
Math has evolved by constantly changing starting
points. Here's more of an algebra example. For
a long time, mathematicians believed that every
number, when squared, must be positive. That
seems obvious, until someone asked, what if we
allow a number whose square is negative? Call
it i, where i squared equals negative 1. Well,
at first, it sounds impossible. But once that
idea is accepted, an entirely new system opens
up. It does not replace what came before. It
expands it. It did not just expand algebra. It
expanded our number system. It created another
new world to do math. The complex plane. The
original system was not wrong. It just was not
complete. So what does this mean beyond math?
Certainty does not just show up in equations.
It shows up in how I see the world. And when
I look back on my life, I notice my thinking
begins to shrink when I assume my perspective
is the correct perspective. I close the door
to possibilities I cannot yet imagine. To ideas
that do not seem possible, at least from where
I'm standing. But math tells a different story.
Math is a history of expanding what we once thought
was impossible. And doing math invites a different
posture to keep exploring, keep asking, keep
listening. It invites us to sit in tension, not
to avoid it. Yes, certainty can give clarity,
but it can also limit what I'm able to see. And
when I begin to notice that, I realize the way
I see the world is not just about the world.
It is shaped by how I've learned to think. So
my questions today are, where might my certainty
be closing my mind? What assumptions am I holding
onto that are keeping me from seeing something
more? something bigger, something more beautiful.